Black lines where a transparent mesh intersects
Up the Max bounces under Render > Light Paths > Transparency to a high number, even numbers like 48 or higher. The more overlapping transparent surfaces there are the more likely to get black artifacts if the transparency bounces isn't high enough.
If that doesn't work, perhaps check the normals aren't getting inverted mid-way, but it's likely the former.

You could also disable the cloth rendering completely by unticking everything under the Object Panel > Cycles Settings, which should speed up the render.